The negative effect of border opening can't be compared to the economic benefits of opening of border as it brings bring down price of goods and services
Actually. Keeling the borders of the country opened and having a net positive flux of immigrants moving to the country would make some good and services to increase in price through time. In the case of countries like the United States, a good example is the cost of house, apartments and shelter in general. Which would also translate to the increase of price of renting a place to live.
As people move in, regardless of their social status and income, they all need a place to stay, the more demand and the same offer will inevitably translate to an increase in price, as the demand won't stop any time soon as the USA continues to be an attractive destination for people from developing countries, then it is save to say homed won't decrease in value.
Also, in the country people are moving to do not have enhanced infrastructure in hospitals and in their crop production, they would be also dealing with inflation in medical services and the price of food. The same logic of supply and demand. In the case of the USA, they have very good food production and infrastructure compared to other nations.